The first person seized by robber getting closer (7)
I believe the answer is:
Here is my best explanation:
'closer' is the definition.
(I've seen this before)
'the first person seized by robber' is the wordplay.
'the first person' becomes 'i'.
'seized by' indicates putting letters inside.
'robber' becomes 'mugger' ('mugger' can be a synonym of 'robber').
'i' inserted within 'mugger' is 'MUGGIER'.
'getting' is the link.
(Another definition for muggier that I've seen is "closer".)