We don't have synonyms for tied house yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are tree house, field house and the house.
(n) :
(UK) 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, and which therefore is obliged to purchase a certain percentage of its stock from said pubco.
(n) :
(UK) 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, and which therefore is obliged to purchase a certain percentage of its stock from said pubco.