As a general rule, it's the Landlord's responsibility to ensure that the property is pest free at the time that the occupancy commences, and to keep it that way unless the nature of the problem is something to which the tenant has contributed.
For example, a mouse / cockroach infestation is typically contributed to by tenants' poor housekeeping, so initial attempts at rectification is their responsibility. I say “initial” as there may be external factors such as in a Strata Building.
So under this criterion in a stand-alone property, the presence of a wasp's nest would not be due to anything that your tenant may or may not have done, so rectification is your responsibility as Landlord.
Don't delay though, as now that you're aware of the problem, if anyone at the property is badly stung, that may make things difficult for you.