No specific number entertained by popular hostelry (3)
I believe the answer is:
inn
'hostelry' is the definition.
(I know that hostelry can be written as inn)
'no specific number entertained by popular' is the wordplay.
'no specific number' becomes 'n' (I can't justify this - if you can you should give a lot more credence to this answer).
'entertained by' is an insertion indicator (inserted letters are hosted or entertained).
'popular' becomes 'in' ('in' can mean trendy).
'n' put inside 'in' is 'INN'.
Can you help me to learn more?
(Other definitions for inn that I've seen before include "Tavern with lodgings" , "Hostelry, tavern" , "One of Lincoln's" , "Pub with lodging" , "Local" .)