Can my landlord in Malta increase my rent whenever they want during my lease?

Generally, no, not unilaterally during a fixed-term lease, since under the Private Residential Leases Act, which governs most residential tenancies in Malta, the rent amount is generally fixed for the duration of the agreed lease term as specified in your written lease agreement, and a landlord cannot simply increase the rent partway through a fixed term without a specific contractual basis allowing for this, such as an agreed rent review clause that was actually built into your original lease agreement from the outset. Rent increases are generally only permitted at specific points recognised under the Act, most commonly at the point of lease renewal when a new lease term is being agreed, or under specific circumstances explicitly provided for in your original lease agreement, meaning your landlord attempting to increase rent mid-term without this kind of proper contractual basis would generally not be enforceable against you, and you would be entitled to continue paying your original agreed rent for the remainder of your current fixed term. If your landlord persists with this improper mid-term increase demand, it would be worth reviewing your specific lease agreement carefully to confirm there's genuinely no rent review clause you may have overlooked, and if there isn't, formally responding in writing referencing your fixed lease terms, with the option of raising the matter with the Housing Authority if the landlord continues to press the improper increase.