If you have incurred the expense as a principal and you are not recovering the expenses as part of any primary supply to your customer, you must charge GST when you recover the amount if the recovery of expenses amounts to a standard-rated supply. It is your business decision on how much you value the supply made when you re-bill the invoice.
However, if you charge a mark-up, the GST treatment for the mark-up is based on the separate supply of service (e.g. arranging fees, administrative fees etc).
For more information, please refer to the e-Tax Guide “GST: Guide on Reimbursement and Disbursement of Expenses” (PDF, 585KB)