Does a priest have to give you a penance following confession?
They should yes give you a penance in confession
(if they do not --ask them for it–it is possible they can forget)
From the Catechism of the Catholic Church: Many sins wrong our neighbor. One must do what is possible in order to repair the harm (e.g., return stolen goods, restore the reputation of someone slandered, pay compensation for injuries). Simple justice requires as much. But sin also injures and weakens the sinner himself, as well as his relationships with God and neighbor. Absolution takes away sin, but it does not remedy all the disorders sin has caused. **Raised up from sin, the sinner must still recover his full spiritual health by doing something more to make amends for the sin: he must “make satisfaction for” or “expiate” his sins. This satisfaction is also called “penance.” **(CCC 1459)
Penance is an integral part of the sacrament of Penance and Reconciliation.
Also… Even if a priest does not give you a penance for whatever reason, your confession is still valid. Receiving a penance from a priest is not necessary for a valid confession. I say this because some worry about validity when their priest does not give them a penance.
True. We do (or should do) penance for our sins apart from the confessional. Whole a priest should impose a penance, confession is valid even of he doesn’t. A bit like he should wear the purple stole but the absolution is not invalid if he does not.