Hello folks I think where the government and spring hooks up broke I was wondering if I could get a replacement for it or do I have to buy a new carburetor.

And it's a carberator to ????

It goes to a poulan pxt16542

 pxt16542 is the model # for the entire machine.  A rider  
 
If your looking for an ENGINE PART, we need the engine make, HP and model #
 
 
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It’s a Briggs and Stratton 16.5 hp the model number is a 31A707

Here's a link to the governor parts assembly:
 
https://jackssmallengines.com/jacks-parts-lookup/manufacturer/briggs-stratton/briggs-stratton-engine/200000-399999-series/31a700-to-31a799/31a707-0874-g5/alternator-controls-electric-starter-governor-spring-ignition
 
What part specifically is broke?  
 
The governor arm has linkage direct to the carb throttle. 
 
The governor arm then has a spring attached to it that goes to the throttle mechanism that
your throttle cable would go to...
.
As you adjust the throttle higher, the spring has more tension on it.
 
There is a separate linkage for the choke.
 
 

It’s the little plastic piece that you hook the governor and spring to the carburetor

That little piece isn't available separately.  
 
Briggs used that piece in many machines...  
 
The tension spring(wraps around the linkage), goes in that little hole on the throttle tab. 
 
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I was afraid of that

If you can find one of those push on clips, small enough to slip tightly onto that linkage, that'd work..