The simple answer to your question is "NO".
There are 4 different kinds of part 135 operating certificate, many of which have a limited number of pilot positions. These pilots must be listed on the paperwork for the certificate and must meet all training, experience and currency requirements as specified by the certificate.
On a Single Pilot Operator certificate, the holder is limited to using only one pilot for all part 135 operations. That specific pilot is listed by name and certificate number on the FAA issued Operations Specification (OpSpec) A040. The use of any pilot(s) other than the single pilot listed on OpSpec A040 is not authorized.
On a Single Pilot in Command certificate, the operator is limited to using only one PIC and up to a maximum of 3 Second In Command (SIC) pilots for all part 135 operations. The PIC and the SIC(s) are listed by name and certificate number on the FAA issued OpSpec A039. The certificate holder is only authorized to use those pilots in the specific duty positions listed in OpSpec A039. The certificate holder is not authorized to use any other pilots, nor are any pilots allowed to serve in a duty position (PIC or SIC), unless they are listed in that duty position in OpSpec A039.
On a 135 Basic, the operator is limited to a maximum of 5 pilots which includes SICs, but all 5 pilots may serve as PIC or SIC as required as long as they are all so qualified. However, they must still be listed ok the certificate as above and since this type of certificate requires the establishment of approved manuals and training programs, the pilots must also have completed the necessary training and comply with the standards set forth in all operation manuals.
On a 135 Standard, there is no pre-set limit to the size of the operation, but all pilots must be listed on the certificate as above and comply with all required training and manuals as above.
Basically, an operator can't just bring in a pilot to fill-in for a single mission. If their own pilots or aircraft are not available for the job, then their company is not available for the job. They would need to sub-out or recommend the client to another certificated operator whose plane and pilot(s) are available.