Do I need parents' permission to renounce?

You can meditate full-time for 12 months, as a layperson, somewhere.

Possibly, after 12 months you will not enjoy full-time meditation and return home.

However, if after 12 months of meditation you attain stream-entry or higher then you will have a liberated mind to help you consider your situation more clearly.

Simply ask them, good householder son. To give permission or not, is up to your parents' choice and goodness.

As for skillful desires to seek the holy life, one is wise not to wait and hesitate even some minutes as unskillful mind and doubts may quickly arise again and it's uncertain if it would be possible anymore tomorrow.

So, best wishes and don't waste time in thinking all around for no work, neither here, nor there, would be done: a waste of precious time.

Tell them "I do not work from now on, and I'll live at the temple forever (as a layman)." Or don't tell anything, just leave them by tell them "I will take a trip".

Then go to Pa-Auk meditation center in Burma to meditate the meditation as a layman.

When the time gone by, they will allow you to renounce.

And you may have get a trick to renounce at there.

Don't forget that, they can live in the temple when you renounced. You or your family should be worried about the future.

Just giving my two cents. Being an Indian daughter myself I have had the same questions knowing it “is” my duty to serve them. This is supported by Buddha- we “have to” serve our parents and they are considered so deserving of respect that even a bhikku can beg for food for their parents. You can ask a teacher the question about “How to serve our parents?” Some say sending metta and inviting them to the path is the highest form of service.

However separations are painful. And it really depends upon not just your desire to renunciate but also what renunciation really means to you. For some like me I know my real practice will only begin when I “physically” leave because only then I can really detach from the material world- I have such attachments (to people). If your conscience and your practice guides you and “accepts” your decision to “physically” leave then maybe do it. It may be helpful to take the guidance and help of a teacher. But do pay attention to the real meaning of renunciation which is non attachment.

Another option is to go to these courses off and on for a month, for a few months and slowly prepare your parents for it so they don’t feel the suddenness of it. It really depends upon how your mind deals with the challenges that come up and whether your conscience can accept your decision of leaving. I for example would need all close ones to agree before I can take any such step otherwise it bothers my mind and goes into ethical questions like “did I abandon my loved ones? Did I not do my duty” etc. Such rumination doesn’t help either.

Best wishes, may you grow in Dhamma.

This is a painful dilemma for all Indian sons with traditionally strong sense of responsibility towards parents. The problem becomes compounded by the fact that there are no support systems for old people in India. This was a very painful issue with me too but I was always clear that I had to take care of my parents. Secondly, monkhood is no guarantee for liberation while intense practice is. So, I think increase the time you spend in meditation. Go for retreats as often as you can. Your karma will then find a way out for you. But do take care of your parents. They have none except you and you would definitely not like to leave them in the lurch. Incidentally, I am a doctor but lost both my father and mother recently in quick succession to the second wave of Covid in New Delhi. It was very painful but I have the consolation that I was at their bedside as they passed away peacefully. I take it as an important aspect of my shila and, therefore, an integral part of my spiritual journey.

I hope that helps. Metta dear friend.

The other answers have offered good advice, opinions, and perspective. I want to bring up two things:

The Buddha's father didn't want him to renounce

The Buddha's parents themselves did not want the Buddha to become a monk. You might read up on that story: https://en.wikipedia.org/wiki/Great_Renunciation. There are varying accounts. I'm not clear on whether he got permission or not. But he did ask for it. And I think he asked for it multiple times.

Monks aren't the only arahants

Lay followers have been able to achieve great peace and wisdom and even arahantship. Consider the praise the Buddha gave to Hatthaka of Alavi, who I think was a businessman. https://www.accesstoinsight.org/tipitaka/an/an08/an08.023.than.html

So, even if you do not ordain, don't despair. There is plenty you can do without taking on robes.

Furthermore, as @LetsBuddhism suggested in his comment, plenty of monasteries aren't that good. Or verse 61 of the Dhammapada:

Should a seeker not find a companion who is better or equal, let him resolutely pursue a solitary course; there is no fellowship with the fool.

You may find a lot of fruit/benefit from looking for a good teacher who practices and teaches good dhamma. And you may find that you do plenty without taking robes.

Children are not for the purpose of being a servant to an old person.

I tell you, monks, there are two people who are not easy to repay. Which two? Your mother & father. Even if you were to carry your mother on one shoulder & your father on the other shoulder for 100 years, and were to look after them by anointing, massaging, bathing, & rubbing their limbs, and they were to defecate & urinate right there [on your shoulders], you would not in that way pay or repay your parents. If you were to establish your mother & father in absolute sovereignty over this great earth, abounding in the seven treasures, you would not in that way pay or repay your parents. Why is that? Mother & father do much for their children. They care for them, they nourish them, they introduce them to this world. But anyone who rouses his unbelieving mother & father, settles & establishes them in conviction; rouses his unvirtuous mother & father, settles & establishes them in virtue; rouses his stingy mother & father, settles & establishes them in generosity; rouses his foolish mother & father, settles & establishes them in discernment: To this extent one pays & repays one's mother & father." https://www.accesstoinsight.org/tipitaka/an/an02/an02.031.than.html

They are afraid of old age because they didn't train to fortify their mind. If you follow their advise you will also be afraid of old age and will want servants of your own.

Your parents would do well in supporting you now, you should try to work with them as a team and have everyone self-develop critical thinking, meditation, ponder views and learn science of physics & behavior to what extent possible develop intellect & good behavior.

It is not wrong to be cautious, critical and pragmatic to protect yourself and your team. A bhikkhu can act like a layman and a layman can act as a bhikkhu, think for yourself and work with your people.