Minding, or keeping an eye on, subsequently (7,5)

I believe the answer is:

looking after

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'minding' is the definition.
The answer and definition can be both to do with social activities as well as being present participle verbs.
Perhaps there's a link between them I don't understand?

'keeping an eye on subsequently' is the wordplay.
'keeping an eye on' becomes 'looking' (I am not sure about this - if you are sure you should believe this answer much more).
'subsequently' becomes 'after' (I've seen this before).
'looking'+'after'='LOOKING AFTER'

'or' is the link.

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I've seen this clue in the Evening Standard.

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