Firm with old student who's trendy (4)
I believe the answer is:
cool
'trendy' is the definition.
(I know that trendy can be written as cool)
'firm with old student' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'with' says to put letters next to each other.
'old' becomes 'o' (abbreviation).
'student' becomes 'l' (as in L-plates for learner drivers).
'co'+'o'+'l'='COOL'
'who's' is the link.
(Other definitions for cool that I've seen before include "Moderately cold" , "Hip - not warm" , "Free of heat; laid-back" , "Calm and unemotional" , "Sangfroid" .)