The definitive answer is to be found in the Piper PA38-112 Maintenance Manual Chapter 4 - Airworthiness Limitations, Table 401. It is also stated in the FAA Type Certificate Data Sheet for the aircraft.
It states that the 'Wing and Associated Structure' has a life of 11,000 flight hours - all airframe serial numbers.
Airworthiness Limitations (and Airworthiness Directives) are mandatory in the UK/EASA.
The 'associated structure' is the carry though stucture in the fuselage to which the wing attaches as far as I know.
There were various wing spar extension options offered by third party companies such as:
Sterling Aviation Technologies :: Wing Life Extension
They claim that it is EASA approved so you may be okay. The cost of the kit plus the labour to install it may prove it to be financially not viable.