Longman Dictionary of Contemporary English
Wiktionary
n. (context UK English) A public house which is either owned by a brewery, or other holding company, and run by a manager, or rented and run by a tenant, or perhaps contractually tied because of loans from a brewery, which therefore is obliged to purchase a certain percentage of it's stock from said pubco
Wikipedia
In the United Kingdom, a tied house is a public house required to buy at least some of its beer from a particular brewery or pub company. That is in contrast to a free house, which is able to choose the beers it stocks freely.
A report for the UK government described the tied pub system as "one of the most inter‐woven industrial relationships you can identify in the UK, with multiple streams of payments running in both directions, from the pub tenant to the pubco and vice versa, generally negotiated on a pub‐by‐pub basis."