If a forthcoming trip is Royal Family related e.g. Jubilee celebrations it would be easier for the Met to provide security for them - it would compromise the security of an event if they had to coordinate with a private team for Harry.
If the trip is private then he can pay for private security, just as a lot of high-profile people do. There are many firms that provide ex-Met and forces to high profile rich families of oligarchs, celebrities, business people, etc.
The Met shouldn't be for hire, because that's what it would be, even for a prince.