When ultimately stuck, make request (3)
I believe the answer is:
ask
'request' is the definition.
(to ask is to request something)
'when ultimately stuck' is the wordplay.
'when' becomes 'as' (eg 'when I walked' means 'as I walked').
'ultimately' indicates one should take the final letters.
The final letter of 'stuck' is 'k'.
'as'+'k'='ASK'
'make' is the link.
(Other definitions for ask that I've seen before include "Inquire" , "Make enquiry" , "Put a question" , "Something demanded" , "Issue invitations" .)