GST on hire charge

Yes, As per section 7(1)(a) is form of supply and schedule (II) includes hiring and it is "Supply of service". Supplier is liable to charge GST on it.

Recipient ( you client) is eligible to claim ITC on it. Because it use in further of business.section 17 of CGST Act 2017, allow input on vehicle which is used for transportation of good.

For rate of tax please refer HSN code