Fathead shown the way, but simply bolted (4)

I believe the answer is:

fled

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'simply bolted' is the definition.
'fled' can be an answer for 'bolted' (I've seen this in another clue). I am not sure about the 'simply' bit.

'fathead shown the way' is the wordplay.
'fathead' becomes 'f' (head letter of 'fat').
'shown the way' becomes 'led' (I've seen this in another clue).
'f'+'led'='FLED'

'but' is the link.

Can you help me to learn more?

(Other definitions for fled that I've seen before include "Ran off in a hurry" , "Female showed the way and escaped" , "Left the field" , "Did a runner" , "Ran or hurried away" .)

I've seen this clue in the Evening Standard.

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