After the destruction of his Nimbus 2000, Harry received a Firebolt as a Christmas present.
Is the Firebolt the last broom he received, or did he get a newer broom during the course of the books?
The Firebolt is the last broom he received during the series, although it seems to be lost by the end.
In The Battle of the Seven Potters (chapter 4 of Deathly Hallows), Harry’s broom falls from Hagrid’s bike as they’re attacked by Death Eaters:
They never go back to retrieve the broom, and the Firebolt is never mentioned again. Harry never owns another broomstick during the final book (unless you count the one he uses in the Room of Requirement).
However, given that Ginny goes on to play Quidditch professionally, I’m sure Harry would buy a replacement broom eventually (and probably use it to play/practice with the kids).