If the prior lease (or a separate agreement) included a monthly (or otherwise regular) payment for the garage, that was a legitimate debt and you are obliged to pay it. If the current lease also includes such an additional payment it will have to be paid as agreed. If it does not, then no such payments will be owed in future. If the current lease references the terms of the previous lease, and bases the current terms on the previous terms, that may include a garage payment without specifically mentioning it in the current lease.
Thre question mentions "partial payment". The tenant will be liable for all agreed payments for the garage (and for anything else) under the old lease for its full term, until it expired, that were not previously paid. Once all such payments have been made there shold be no further payments owing, except whatever was agreed to in the new lease. Those payments will be due as agreed.