How long it took for your fears to be dissipated (4,5)

'fears to be dissipated' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'how long it took for your' is the wordplay.
I cannot really understand how this works, but
'it' could be 'e' ('e' can mean 'electronic' which is similar to 'IT') and 'e' is found in the answer.
an anagram of 'your' is 'oury' which is located in the answer.
'long' could be 'far' (similar in meaning) and 'far' is found within the remaining letters.
A single letter 's' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?