Obligate with an out-of-the-way offer (4)
I believe the answer is:
bind
'obligate' is the definition.
(thesaurus)
'an out-of-the-way offer' is the wordplay.
'an out of' means one lot of letters goes inside another.
'the way' becomes 'n' (Compass direction - North).
'offer' becomes 'bid' (bid is a kind of offer).
'n' inserted within 'bid' is 'BIND'.
'with' is the link.
(Other definitions for bind that I've seen before include "Wrap tightly - nuisance" , "Impose a contractual obligation on (someone)" , "Tie up; annoyance" , "Senior figure" , "Restrict" .)