They could ask, but why would you? I assume this is an external solicitor, not an employee. Some context would probably be helpful.
Council wont pay a solicitor to send a letter to a neighbour. Councils have their own capacities and can issue their own letters and wont charge you for that. Councils can request certain acts and if someone declines to act council can even access the site and cut trees and impose a charge to the land owner or initiate penalties etc.
Not trees but, how effective is an order from the Council; Council has served notice on our neighbour to clean up his property, we are watching with interest to see what happens, so far - nothing. He has been ordered to remove the bamboo which is out of control at the back of the property and he has never mowed the grass since we moved here, my son mows his grass verge because we cant stand how it looks. He did spread mulch over the grass in an effort to stop the growth but doesn't realise he needs to put a barrier between the grass and the mulch with the result the grass grew longer after another visit from the Council there was a second load of mulch delivered yesterday still sitting there as the grass grows longer. I can see the funny side but I am glad we have fully grown shrubs which hide his front yard from from any visitors to our house while we wait to see what happens ... it will be interesting to see how far the council will go to enforce the order ...
It's well over the height of a 2 storey house ... it has begun to invade our neighbour's backyard at our mutual fenceline and I am concerned about it invading our backyard ...
No, I see no reason why you should incur any cost (other than your rates notice) for council to act against a troublesome neighbor that is likey in breach of local council rules. I cleared out a house and cleaned up the yard of a hoarder (Sydney). Council had been at them for years after neighbors complaints (mostly about the rats and smell, we were finding a dead rat every 5min for 6 days !). It was only after the owner/occupant was legally declared incompetent (largely mentally) and unable to look after themself (late 50's) that things started to happen. Even then it all still had to go before a judge, with all the attempts to contact family and have them deal with things failing, it was handed off to the State Trustees who finally sorted it out (working with council) some 6 months later Proceeds from the property ($3+m) and asset sale (very little recoverable) to cover costs incurred, then toward care of the person. If you didn't know everything with council takes longer, and when it goes legal it takes an eternity
Had a branch of the street tree at the front of the house fall at 1am this morning. I shifted it off the footpath and away from danger. I rang the Ranger before 8am, he arrived while we were still on the phone (he was already on the way over). We had a chat, arranged for the chippers and it was gone by 10.30am. Great to have an efficient council (on the odd occasion).