Sentient computer following subordinate for a moment (4-6)

'sentient computer following subordinate' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'moment' is the wordplay.
I cannot quite understand how this works, but
'moment' could be 'second' (synonyms) and 'second' is found in the answer.
The remaining letters 'half' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'for a' is the link.

Can you help me to learn more?