Caravan Undifferentiated
Flight Crew Commercial
Situational Awareness; Communication Breakdown
Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Took Evasive Action
Human Factors; Procedure; Environment - Non Weather Related
We [took off] and asked for flight following. ATC couldn't see us under 2;000 feet; but we continued talking to them.  I told them we would climb to 3;000 and pickup following. Just getting ready to ask for following; we heard a [single engine aircraft] coming off ZZZ so we were looking and making the calls for position; altitude and intentions. We made another position and altitude call at 3 miles North.  Traffic Alerting System (TAS) picked him up and alerted when he was already a danger at 1 mile North of mid-field; and did not pick him up prior.  We started to break right to position when he reported he was 3 miles and 2;800. [The Captain] told him to stop his climb three times; as he banked right; I caught him crossing our nose so we banked hard left as he passed under; possibly just outside our right wing.  We were at 3;000 feet; 1;400 above TPA for a mid-field crossing direct to ZZZ1. [The Captain] checked our passengers and then asked the other pilot if they were ok. He stated; 'ya luckily the other guy saw us first.' I told him that was me; and etiquette would be if you don't have traffic in sight to delay your climb.  He apologized and stated he never saw us. [The Captain] said;' thank you; Have a nice day.'  We continued on to [destination] without further incident.  Fly at a higher altitude so as to be in radar contact with ATC for adequate flight following for separation and traffic. Upon hearing other traffic at an uncontrolled airport that we are overflying; make direct contact with them to ensure spacing and understanding of intentions.
The Pilot of an Air-Taxi operation reported a near-mid-air-collision with a single engine aircraft that was climbing out of a non-towered airport. The Air-Taxi pilot was making position reports; but the other departing pilot was not be making reports. The Traffic Alerting system provided notification which allowed for evasive action to prevent a collision.