Real Dictionary

tie up
phrasal verb: If someone ties another person up, they fasten ropes or chains around them so that they cannot move or escape.
phrasal verb: If you tie an animal up, you fasten it to a fixed object with a piece of rope so that it cannot run away.
phrasal verb: If you tie up an issue or problem, you deal with it in a way that gives definite conclusions or answers.
phrasal verb: When you tie something up, you fasten string or rope round it so that it is firm or secure.

tie up in American English
to fasten securely by tying
to tie firmly or securely

tie up in British English
to attach or bind securely with or as if with string, rope, etc
noun: a link or connection

tie-up
countable noun: A tie-up or a traffic tie-up is a long line of vehicles that cannot move forward because there is too much traffic, or because the road is blocked by something.

tie-up in American English
a temporary stoppage or interruption of work, production, traffic, service, etc.
noun: a temporary stoppage or slowing of business, traffic, telephone service, etc., as due to a strike, storm, or accident

tie-up in British English
noun: a business connection that has been arranged between two organizations