Has a hereditary peer ever been promoted or demoted to a higher or lower rank?

Wikipedia gives a warning of the risks inherent in trying to demote a noble. Machiavelli later warned that it was safer to kill a disloyal noble than to humilate and/or impoverish him.

Henry [Bolingbroke was the son of John of Gaunt, Duke of Lancaster, himself the son of Edward III. ... Henry was involved in the revolt of the Lords Appellant against Richard in 1388, resulting in his exile. After Gaunt died in 1399, Richard blocked Henry's inheritance of his father's duchy. That year, Henry rallied a group of supporters, overthrew and imprisoned Richard II, and usurped the throne, actions that later would lead to what is termed the Wars of the Roses and a more stabilized monarchy.

Later edit I just found a classic example of two nobles being demoted; it doesn't end well.

Surrey, along with many of King Richard II's advisors, was arrested after the King's deposition by King Henry IV in 1399. In the end he had to forfeit the honours and estates he had gained after the arrests of Gloucester and Arundel, in particular the Dukedom of Surrey, although he retained the Earldom of Kent. Early in 1400, Kent, along with his uncle, the Earl of Huntingdon (no longer Duke of Exeter), plotted to kill King Henry IV and free King Richard II from prison and return him to the throne. This "Epiphany Rising" failed and Kent was captured and executed.

Famous computer programmer Ada Byron was married to William King, the Baron King. He was then promoted to Earl Lovelace in Queen Victoria's Coronation Honours List, making Ada the Countess Lovelace (which is why she's often called Ada Lovelace, though she shouldn't be).

Peers have often been promoted by being granted another peerage with a higher rank.

In some cases, a peerage can be inherited by someone who already holds another peerage title.

So a number of peers have accumulated several different peerage titles with the same or different ranks.

Edmund Mortimer of Wigmore was created Baron Mortimer of Wigmore by being summoned to Parliament in 1295. His son Roger Mortimer, the second baron, became the lover of Queen Isabella. They gathered an army in France and invaded England in 1327. They forced King Edward II to abdicate in favor of his and Isabella's young son Edward III. Isabella became the official regent for her son, but Roger Mortimer was promoted to Earl of March and really ran the government. It was announced that he ex king Edward I died "of natural causes" while imprisoned, but he was commonly believed to have been murdered.

So it is not surprising that young Edward III overthrew Mortimer a few years later. Mortimer's property and titles were forfeited and Mortimer was exceuted.

The second time, it was created as a re-grant; The son of the 1st Earl of March, Edmund de Mortimer, was summoned to parliament on 20 November 1331. The second baron of this creation became Earl of March in 1354 upon the reversal of the attainder. The two titles then merged. The barony either merged in crown in 1461 or became extinct in 1425.

https://en.wikipedia.org/wiki/Baron_Mortimer_of_Wigmore

Thee are other examples of attainders being reversed and the heirs of executed nobles getting some or all of their property and titles back.

And I think that examples could be found of the son or grandson of an executed noble getting back a lesser title but not a higher title. So that could be considered a demotion in peerage rank. But that not would not be a demotion in rank for a single noble, but a demotion for different generations of the noble family.

Something which almost fits the definition of a demotion happened to a Duke of Norfolk.

Thomas Howard, the third Duke, fell out of favour with the dying Henry and was attainted on 27 January 1547; he was stripped of his titles and his lands reverted to the Crown. Imprisoned in the Tower of London, he narrowly escaped execution through Henry's death the following day, but remained imprisoned until the death of Edward VI and the accession of the Catholic Queen Mary to the English throne in 1553, upon which his lands and titles were restored to him.

https://en.wikipedia.org/wiki/Duke_of_Norfolk

But Queen Mary I restored him to his dukedom, so he can't be considered to have been demoted in peerage rank. And his survival for so long after being attainted and condemned to death was a rare miracle, so I doubt if any British noble was ever stripped of their rank and then restored to favor and given a lesser noble rank.

An expert on the subject might be able to think of an example.

Someone who illustrates both aspects of the question is Thomas Wentworth, 1st Earl of Strafford who as an adviser to Charles I, progressed from Baronet, through Baron, Viscount and Earl, to being executed and his titles reverting to the crown.

In a fairly recent example, Alan Brooke was made Baron Alanbrooke in 1945 and Viscount Alanbrooke in 1946. I don't know for sure why he was promoted after a year, rather than being made a Viscount from the start, but it may have been something to do with his more famous subordinate Montgomery being made a Viscount in early 1946.

Wikipedia's list of trials of peers in the House of Lords shows that this was only for capital crimes, and all those found guilty were executed, except for five who were able to claim "privilege of peerage" to escape punishment for a first offence.

Several Germans were stripped of their British titles by the Titles Deprivation Act 1917, as a result of fighting on the German side during WWI. While the act provided for them to petition to have their titles restored after the war, none have ever done so.

The usual way of depriving someone of titles before the modern era was via attainder, which condemned the subject to death, with forfeiture of both property and titles, depriving them of the ability to pass anything on to their descendants. This makes it unlikely that any peer has ever been demoted, although some swore oaths of loyalty and had their property and titles restored.

Yes to the first.

Examples: the 1st Marquess of Montrose had inherited the title of Earl of Montrose from his father. The 4th Earl of Devonshire was made a Duke for his support of William III in the 'Glorious Revolution'.

I suspect that someone who had done something bad enough to be stripped of their peerage would not simply be reduced in rank.