Very light, perhaps, the cost of travelling around Lima (5)
I believe the answer is:
flare
'very light perhaps' is the definition.
(very light is a kind of flare)
'cost of travelling around lima' is the wordplay.
'cost of travelling' becomes 'airfare' (I've seen this before).
'around' means to look at the middle letters.
'lima' becomes 'lare' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The middle letter of 'airfare' is 'f'.
'f'+'lare'='FLARE'
'the' acts as a link.
Can you help me to learn more?
(Other definitions for flare that I've seen before include "Blaze; distress signal" , "Sudden burst of flame" , "Feral kind of sudden activity" , "Burn with sudden brightness" , "(Burn with) sudden blaze" .)