Major work such as tree lopping is usually carried out by the lessor or agent as part of their obligation to maintain the property in good repair.
Day-to-day garden upkeep, like mowing, weeding and light pruning, generally falls to the tenant where the tenancy agreement provides for it. The dividing line is usually the scale and safety of the work involved.
When in doubt, talk to your property manager before any work starts. Clarifying responsibility up front keeps the garden healthy and avoids disputes between owners and tenants.
