One's broadcasting time, so long at first, kept within limit (5,7)

'one's' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'broadcasting time so long at first kept within limit' is the wordplay.
I cannot really understand how this works, but
'broadcasting' could be 'radio' (radio is a kind of broadcasting) and 'radio' is present in the answer.
'time' could be 't' (abbreviation) and 't' is found in the answer.
'at' could be 'on' (location) and 'on' is present in the answer.
'first' could be 'i' (I in Roman numerals eg Elizabeth I) and 'i' is located in the answer.
The remaining letters 'sat' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?