Pastime that’s welcome, occupying page in recent Times (9)
I believe the answer is:
philately
'pastime' is the definition.
(philately is stamp collecting)
'welcome occupying page in recent times' is the wordplay.
'welcome' becomes 'hi' (I've seen this in other clues).
'occupying' means one lot of letters goes inside another.
'page' becomes 'p'.
'in recent times' becomes 'lately' (synonyms).
'p'+'lately'='plately'
'hi' going inside 'plately' is 'PHILATELY'.
'that's' is the link.
(Other definitions for philately that I've seen before include "interest in stamps" , "stamps territory?" , "Collecting little stickers" , "Study of postage stamps" , "collecting small items that may grow in value" .)