Pub that’s popular: Nag’s Head (3)
I believe the answer is:
inn
'pub' is the definition.
(thesaurus)
'popular nag's head' is the wordplay.
'popular' becomes 'in'.
'head' indicates taking the first letters.
The initial letter of 'nags' is 'n'.
'in'+'n'='INN'
'that's' is the link.
(Other definitions for inn that I've seen before include "Country pub, often with accommodation" , "pubs?" , "Local" , "Jamaica, for one" , "One of Lincoln's" .)