Gonna describe the issue with an old gun, if someone would know which part is worn out....

Came across and old Police model in 38 S&W (pre-war). The action times right if you shoot double action. If you shoot single action then the cylinder won't quite turn far enough to lock in place before the hammer drops.

Thanks for any responses.

In a Smith there is a part known as the "hand" that transfers trigger pull to the cylinder that will wear and cause timing issues. I'm sure a Colt is Similar but have never opened one.

I had to correct the original post. I had it backwards. The issue with shooting single aciton....the cylinder doesn't quite turn far enough.

First, pull the cylinder and clean and lube it.

If no joy,

1.  Cock gun slowly.  Does it lock in place?

2.  Cock gun very quickly.  The idea is to get the cylinder moving fast so it has some inertia.  Does it lock in place?

If #1 fails but #2 succeeds, probably need a new hand.

This.  And that's not a job for the amateur.  Old Colts were hand fitted.  They are not the easiest thing to work on and finding a good part may be a challenge.  The old Colt lockwork had a reputation for being "soft" and with hard use could get out of time.

Tried to work on this old Colt myself. Timing issues. Failed. Sent it off to Frank Glenn in AZ and he got it perfect, hopefully for a very long time. Quality work costs $$$.

If the Colt is a .38 S&W/Colt New Police, it's a Police Positive model.
The same gun with a longer frame and cylinder for use with .38 Special is a Police Positive Special.

The classic Colt out of time condition is when the hammer is slowly cocked in single action the hammer reaches full cock but the cylinder is not locked and a slight push will rotate it to lock.

This is a worn hand.
In the old Colt's the hand was considered to be a normal maintenance part that would need to be refitted or replaced after a good bit of use.
AS LONG as the cylinder is pushed into full lock when the trigger is pulled, the Colt is safe to shoot.

The normal repair is to stretch the hand.  NOTE: this is NOT done where or how you would think.
Before attempting find out the correct procedure and tool to use.
Also note that sometimes when attempting a stretch the hand will just shatter.
Another note: Colt hands can only be stretched ONE TIME.  
This work hardens the steel and a second attempt almost always breaks the hand.

To stretch a hand get a 1/2 inch wide chisel and grind the end flat.  Polish the end and round off the sharp edges.
Put the hand on a steel bench block and put the chisel on the slot on the inside-bottom of the hand where it's thin.
Carefully keeping the chisel at 90 degrees to the hand, tap the chisel with a small hammer.
This will stretch the hand if done correctly.
Stretch a tiny bit at a time to prevent going too far.

After stretching stone the area to clean up any chisel marks or roughness but DON'T remove ANY metal.

If the hand breaks, cracks, or has been previously stretched, the only option is to fit a new hand.
Jack First Gun Parts manufactures high quality replica hands for some of the old Colt models.
Used hands will very seldom work, and even those are almost impossible to find.   Buy a new Jack First part.

I strongly recommend buying a copy of the Jerry Kuhnhausen Shop Manual, Volume One on the Colt Double Action Revolvers.
This was written as a training aid for new pistolsmiths and shows all Colt pistolsmithing to factory standards and methods, no jackleg work.
Among the procedures are photos of hand stretching and the altered chisel.

As above, if you want it repaired right and at an excellent price and turnaround, Frank Glenn is a Master Colt pistolsmith and an American Handgunner Magazine Top 100 American pistolsmith............

https://www.midwayusa.com/product/1014291858?pid=369326
Brownell's is out of stock.

http://glenncustom.com/