usually grants dont't take very long to be approved. the last time we applied, it took about 1-2 weeks. if you need to await the apply for your grant, you can actually call up HDB and tell them about it. They can cross-check with the department processing your grant application to check the status and if it is necessary, they will postpone your 1st appointment until you get your grant approved.
for us we reapplied our HLE, and it couldn't make it on time so we called and asked to change our appointment.
hope this helps.