Obligate with an out-of-the-way offer (4)
I believe the answer is:
bind
'obligate' is the definition.
(I've seen this in another clue)
'an out-of-the-way offer' is the wordplay.
'an out of' indicates putting letters inside (some letters on the outside of others).
'the way' becomes 'n' (Compass direction - North).
'offer' becomes 'bid' (synonyms).
'n' inserted inside 'bid' is 'BIND'.
'with' acts as a 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" .)