Changing troops in first line during battle?

This concept is actually regarded as one of the key advantages of the Roman Manipular line of battle compared to the Greek Phalanx. When the front line of maniples were starting to tire the 2nd line would advance through the gaps between the first line. This would be repeated through the course of the battle, slowly pushing the enemy backwards with each leapfrog.

John H. Gill's 1809 - Thunder on the Danube, Vol. I on page 193 describes St. Hilaire employing this stratagem during the battle of Teugn-Heusen, April 19, 1809. The 3rd Ligne attacks the Austrians first in a pinning attack; followed by a more serious assault by the 57th Ligne that captures and holds the Buchberg. Meanwhile the 3rd Ligne reforms and with the 10th Leger, 72nd Ligne and 105th Ligne launches a third wave that pushes the defending Austrians first through and then out of the neck of woods between the Buchberg and Hausen.

The usual variant on the stratagem was for a second line to advance through the gaps in the first line, this being regarded as safer than having the first line attempt to disengage while still in primary contact with the enemy.

Another standard use of this stratagem is the use of light cavalry to cover a retreat. The light cavalry charges through the gaps in the infantry line and engages the enemy long enough to allow safe disengagement by said infantry. Next the cavalry disengages and reforms some hundreds of yards back to freeze the enemy advance, before itself withdrawing. No Napoleonic or Frederickian commander could be regarded as competent who did not have this tactic in his kit.

The Charge of the Heavy Brigades (Household and Union) at Waterloo is another classic example of how to employ this stratagem to effect. Both D'Erlon's I corps and the British heavy cavalry are effectively hors de combat for the remainder of the afternoon, but the consequent limiting of Napoleon's options buys Wellington more time.

Update:
The evolution of tactics from the Frederickian linear model to the Napoleonic battalion model is nothing less than a modern example of the evolution of the Greek phalanx into the Roman maniple, and then cohort. It created gaps in the line that were too small for the enemy to make effective use of, but through which friendly artillery, cavalry and relieving infantry could advance to allow the original line to disengage.

In the latter part of the 20th century this stratagem migrated all the way down to the squad level; one sees it in use during the standard squad leapfrog so popular in WWII movies, where half the squad provides covering fire while the other half advances, and then the roles reverse.

Update #2 - The Conquest of Gaul:
In Chapter 5 (of my translation) Failure in the Alps (57 BC), 4th paragraph, Caesar writes:

... But what told against them [Caesar's forces] was that the enemy, when exhausted by prolonged fighting, could retire from the battle and be relieved by fresh troops, which our men could not do on account of their small numbers; not only had tired men to stay in the fighting line, but even the wounded had to remain at their posts without any chance of respite.

... and Baculus - the chief centurion who was disabled from several wounds in the battle against the Nervii - came running to Galba ... and told him that their only hope of escape was to try their last resort, a sortie through the enemy lines. ...

Suddenly they charged out from all the gates, without giving the enemy a chance of realizing what was happening or of preparing to meet their onslaught. It was a complete reversal of fortune: the Gauls who had counted on capturing the camp were surrounded and cut off. Of the forces that had taken part in the attack - known to number over thirty thousand - more than a third were killed; the rest fled in terror and were not allowed to rest even in the mountain tops.

Update #2B - The Conquest of Gaul translated by S. A Handford, 1951

Describing the Siege of Alesia, final day, Caesar states (my emphasis):

... The unfavourable downward slope told heavily against the Romans. Some of the Gauls flung javelins, while others advanced to the attack with shields locked together above their heads, fresh troops continually relieving them when they were tired. ....