The short answer to your ...

The short answer to your question is Yes.  However, as some have already mentioned more information is needed.  I do not believe this is a treatment question as many others have assumed, but that would be a next step.

Is this well intended for single private household usage?  Additional requirements may apply for commercial or community usage.

What are the well construction details?  Dug/drilled/bored, casing type and integrity, annular seal integrity, well surface condition?  Basically is the well protected from surface contaminants (surface water entry, animals/insects, vegetation intrusion/tree roots, etc.)?  This is essential to prevent ongoing bacterial contamination.

Has the well been used regularly or left abandoned for an extended period of time?  If the well has been sitting for a while the water within the casing is likely to be stagnant.  Install your new pump and run it for an extended period to develop the well.  You will want to do this even if the well has been used regularly, as introducing your new pump will stir up the water column.  Ideally you should run the pump until the water is clear, which could take several hours. If your well has poor recovery be careful not to run your pump dry.

Once you have sufficiently developed the well, yes, complete the shock chlorination process.  I'm not sure where you are located, but in Canada there are several guidance documents available on the proper procedures.  Generally you add a calculated volume of chlorine bleach based on the well dimensions, run your pump (and household taps if connected to house) until you smell chlorine, allow everything to sit for 12-24 hours, and then flush water to an outdoor area where it can infiltrate into a non-sensitive vegetated area (NOT to a septic system or surface water feature) until chlorine dissipates.

Once chlorine has been fully flushed from the well (free chlorine residual