Having to step lively can be a nuisance (4)

I believe the answer is:

pest

I'm a little stuck... Click here to teach me more about this clue!

'a nuisance' is the definition.
(I've seen this in another clue)

'having to step lively can' is the wordplay.
'step' can be anagrammed to 'PEST'.
But, I am unsure how this is indicated.

'be' is the link.

Can you help me to learn more?

(Other definitions for pest that I've seen before include "Aphis" , "Destructive insect or nuisance" , "Destructive creature" , "Troublesome man or animal" , "Annoying person" .)

I've seen this clue in the Evening Standard.

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