Date: 202008
Local time of day: 1201-1800
Location: ZZZ.Tower, US
Flight conditions: VMC
Weather elements / visibility: 10
Aircraft: Gulfstream IV / G350 / G450
Operator: Corporate
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Climb
Airspace: Class C ZZZ
Reporter organization: Corporate
Reporter function: First Officer; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Human factors: Troubleshooting; Situational Awareness; Distraction
Second reporter function: Pilot Not Flying; Captain
Anomaly: Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Flight Deck / Cabin / Aircraft Event Other / Unknown; Inflight Event / Encounter Bird / Animal
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance; Flight Crew Became Reoriented
Contributing factors: Environment - Non Weather Related; Human Factors
Primary problem: Environment - Non Weather Related

Narrative: The weather leaving ZZZ was clear and winds were calm. Other than a taxi instruction that was incorrect from Ground Control where the controller kept providing a taxi from the North Ramp even though we requested taxi from FBO ramp; the taxi out to the runway was normal. Tower Control took over the taxi instructions prior to crossing the landing Runway of XXR and XXL while we were given instructions to taxi to Runway XY. Runway XY was entered into the FMS (Flight Management System) with the departure. The takeoff briefing was performed as we taxied out identifying a Long Range Nav takeoff and confirming the L Nav selection on the guidance controller. The takeoff was normal at XA:45Z until around 500 ft. above ground level; a wasp was seen coming out from the top of the glare-shield and landed on the hand of the Pilot Flying. It became apparent that the wasp was going to cause issues immediately.Initial focus was to ensure aircraft was just flying but no attention was made to the flight director. We were still flying with wings somewhat level and nose high although later we realized we had turned slightly to the right. The control of the aircraft swapped back and forth from Left to Right-Side Pilot several times as the wasp kept flying around. The Right-Side Pilot finally found a napkin in the cockpit to attempt to kill the wasp and transfer of control went back to the Left-Side Pilot. Finally the wasp was trapped and focus was back to navigating versus just attitude flying. At that point; we noticed that the flight was not on course about the time that Departure asked us our heading. I told them to standby as we finally killed the wasp under the napkin. We were given a heading of 330 which we then initiated only to be later told just to navigate back to the east toward ZZZ1. Moments later; we were informed that ATC wanted a phone call to which I replied that it would be quite some time before that could happen. What we did correctly [was] fly the aircraft. At no point in the takeoff and initial climb out did we lose control of the aircraft while attempting to find and kill our invading wasp. No other traffic was identified nor did the TCAS (Traffic Collision Alerting System) alert us to that issue. What we did not do correctly [was] navigate. The crew kept having to juggle the wasp vs. the airplane in an attempt to not get stung. Not to be taken lightly given different weather and terrain conditions but this one is for the books and for training classes for sure.


Second narrative: [Report narrative contained no additional information.]


Synopsis: Gulfstream IV flight crew reported a wasp was discovered in the cockpit after takeoff.