This person wears coat of Leatherette, sound like a cow hide (3,3)
I believe the answer is:
lie low
'hide' is the definition.
(I know that lie low is a more specific form of hide)
'this person wears coat of leatherette sound like a cow' is the wordplay.
'this person' becomes 'I' (the person writing).
'wears' means one lot of letters goes inside another.
'coat of' suggests removing the centre (only the letters that coat the word).
'sound like a cow' becomes 'low' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'leatherette' with its centre taken out is 'le'.
'i' placed within 'le' is 'lie'.
'lie'+'low'='LIE LOW'
Can you help me to learn more?
(Other definitions for lie low that I've seen before include "Remain unobtrusive - in prone posture?" , "Stay doggo" , "Conceal oneself or one's intentions" , "'Keep out of sight, avoid attention (3,3)'" , "Conceal oneself, don't make intentions known" .)