Real Madrid are very lucky to get world class players for free they've done it with several other players in their squad in seasons before now, Trent is a good signing, a world class RB and that's what they really needed him, atleast that loophole won't be there no more after Trent moves from Liverpool to Real Madrid, it's a big lose to Liverpool since they didn't benefit a dime from Trents transfer.
I believe that the new coach would be pleased with this deal, Real Madrid had to act fast before Liverpool convince Trent to renew his contract and becomes costly in the transfer this summer, atleast they've secured him for free and the RB position is settled for the next incoming coach, it's not as if they signed a developing player, Trent is a world and one of the best in that position.
That's why they're rushing to sign TAA as soon as possible. You get a world class wing back, if you're not serious other club would sign him.
You paid nothing for a world class talent. No reason not to sign him a contract as soon as possible.