Ticklish case in infectious air? One going underground (9)
I believe the answer is:
earthworm
'one going underground' is the definition.
(animal which lives underground)
'ticklish case in infectious air?' is the wordplay.
'case' suggests removing the centre.
'in' means one lot of letters goes inside another.
'infectious air?' becomes 'earworm' (a song or 'air' which gets stuck in your head).
'ticklish' with its centre removed is 'th'.
'th' inserted inside 'earworm' is 'EARTHWORM'.
(Other definitions for earthworm that I've seen before include "Burrowing creature" , "Garden burrower" , "What mole eats" , "Soil-dwelling invertebrate" , "Soil-dwelling creature" .)