Jack in the morning: my, that's lucky! (5)
I believe the answer is:
jammy
'lucky' is the definition.
(jammy means lucky in a smug way)
'jack in the morning my' is the wordplay.
'jack' becomes 'J' (playing card abbreviation).
'in the morning' becomes 'am' (short for ante meridiem - before noon).
'j'+'am'+'my'='JAMMY'
'that's' is the link.
(Other definitions for jammy that I've seen before include "Lucky (and sticky?)" , "Lucky - as conserve" , "Fortunate; sticky?" , "Lucky (informal)" .)