Her new prima donna I smelt it
Kendrick can tell just by her smell, possibly overly gaudy perfume, that she is a prima donna, someone who is vain, arrogant, or generally obsessed with material things.
There is also the pun on prima donna and pre-Madonna by which Kendrick means he sees/smells, that this woman will become famous one day, like Madonna, hence the pun on pre-Madonna and prima donna. Since Kendrick is the new westcoast rap king, he even wants to be her new pre 2Pac, whom Madonna had an affair with.
To help improve the meaning of these lyrics, visit "Memories Back Then" by T.I. (Ft. B.o.B, Kendrick Lamar & Kris Stephens) Lyrics and leave a comment on the lyrics box