Aerostar pilot reported during the climb experiencing left engine turbocharger issues resulting in reduced power at altitude. The pilot continued to their destination airport where they landed safely.

Narrative

On a clear day; I departed ZZZ on an IFR plan at approximately XA:10. The Aerostar 702P aircraft (turbocharged and pressurized) was cleared to FL210. At approximately XA:35 and at 17;000 feet MSL; A pop was heard from the Left Engine and immediately the aircraft yawed to the left. I immediately regained control of the aircraft by disconnecting the KFC200 Autopilot and leveled off the aircraft at 17;000. I advised ATC (ZZZ Center) and I needed a few moments to sort things out. After checking all gauges; instruments and observing out the window that the engine is still running with no visible signs of damage; I determined it best to leave the engine running since it was making some power. The power was reduced; however. In fact; all the engine parameters were within normal limits. I suspected I had lost turbo boost since the engines rely on turbocharges at higher altitudes to maintain full rated power. I suspected additionally; that one of the turbo ducts had come off or burst or one of the turbochargers had failed.After a few minutes; I reported everything appears to be stable after adjusting engine controls for the left engine to run in the normally aspirated mode and that I wish to remain at 17;000 for the duration of the flight and that I would like to proceed direct to ZZZ; my final destination of the day; where ample resources would be available to completely diagnos the problem. My theory was that the Left Engine had gone normally aspirated and at lower altitudes the left engine would regain all of its power back. Going on that theory; after about 20 minutes of stable flight I asked for a decent from 17;000 to 13;000 feet and in so doing I regained additional power on the left engine when the manifold pressure came up an additional 4 inches. After a couple of more handoffs with ZZZ Center; the new controller asked how I was doing and if I was able to restart my left engine. I responded that the left engine was never shut down nor restarted and everything seemed to be doing fine - just with reduced power. He told me that he was going to undo my priority handling and that I should proceed on.At no time for the remainder of the flight did any of the left engine instruments indicate that anything was wrong or out of limits with the left engine. The oil pressure and temperature were equal to the opposite fully operating engine; and all other indications were within normal limits.Upon reaching the terminal area of ZZZ; I advised ZZZ Approach; who handles arrivals into ZZZ; that I MAY not be able to do a 'go around' or missed approach due to possible less power available from the left engine. ZZZ Approach decided to give me priority handling and have the Tower divert all other arrivals/departures to other runways currently in use. I requested to use Runway XXR since it was the closest runway to my intended FBO. My request was granted and both Approach and Tower said Runway XXR was all mine and eliminated all possibility of other traffic interfering with my landing. I conducted the RNAV Runway XXR approach under clear conditions and had no problems with the landing; rollout and short taxi to the FBO.Down at lower altitudes in the terminal area and during the landing phase; the left engine had equal power to the right engine; and it appears that a go around could have been made. I still feel it was prudent to advise Approach Control and Tower of the possible problem of doing a go around. The Approach Control and Tower at ZZZ were very accommodating.It was later determined that the Right-Hand turbocharger of the Left Engine had internally failed which caused loss of turbo boost for higher altitudes. Within a couple of days repairs were effectuated by replacement of the failed turbocharger by a licensed mechanic.