Tailor (tiny and agile) creates warm atmosphere (9)
I believe the answer is:
'warm atmosphere' is the definition.
(genial or cordial atmosphere)
'tailor tiny and agile' is the wordplay.
'tailor' indicates anagramming the letters (I've seen this in other clues).
'and' is a charade indicator (letters next to each other).
'tiny' put after 'agile' is 'agiletiny'.
'agiletiny' with letters rearranged gives 'GENIALITY'.
'creates' is the link.
(Other definitions for geniality that I've seen before include "good humour" , "Cheeriness" .)