Obligation to pursue small bed for dog (7)
I believe the answer is:
scottie
'for dog' is the definition.
(Scottie is an example)
'obligation to pursue small bed' is the wordplay.
'obligation' becomes 'tie' (I've seen this before).
'to pursue' is a charade indicator (letters next to each other).
'small' becomes 's' (abbreviation - e.g. clothes size).
'bed' becomes 'cot' (cot is a type of bed).
's'+'cot'='scot'
'tie' put after 'scot' is 'SCOTTIE'.
(Other definitions for scottie that I've seen before include "Dog" , "Type of terrier" , "animal" , "Breed of terrier" .)