Last from Beat poet seen in this term? (9)
I believe the answer is:
'this term?' is the definition.
(trimester is a kind of term)
'last from beat poet' is the wordplay.
'last from' says to take the final letters.
'poet' becomes 'rimester' (alternative spelling of rhymester).
The last letter of 'beat' is 't'.
'seen in' is the link.
(Other definitions for trimester that I've seen before include "part of college year" , "US academic term" , "Period of three months" , "American term" , "academic session" .)