Modern resort appears regularly in the Times? (9)
I believe the answer is:
newspaper
'the times?' is the definition.
(The Times is a newspaper)
'modern resort appears regularly' is the wordplay.
'modern' becomes 'new' (associated in meaning).
'resort' becomes 'spa' (spa is a kind of resort).
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternating letters of 'appears' are 'per'.
'new'+'spa'+'per'='NEWSPAPER'
'in' acts as a link.
(Other definitions for newspaper that I've seen before include "Publication on folded sheets" , "Broadsheet, e.g." , "Eg, The Times" , "It's (mainly) black and white, and read all over!" , "printed edition" .)