Coin pair are just used to convert between two coins or the currency it is paired with for example if you have usdt on your wallet and you want bitcoin equivalent to that usdt or less than it. You will look for the pair of BTC/USDT and then buy bitcoin. After this what you have on your wallet is bitcoin and not the pair. So to move the bitcoin to another address either exchange or wallet you just transfer using the withdraw option and to the new receiving exchange or wallet address. So there is no such thing as moving a pair.