First, you do not have to discontinue your HDHP policy to accept the HRA. What the HRA does is stop you from contributing to your HSA, so long as you are covered by the HRA.
Well, to be more accurate, any month that you are covered by "conflicting" health coverage like an HRA counts against your annual HSA contribution limit. In your case, if you started the HRA after June 1st (the first day of the month determines coverage for the month), then you would have had HDHP coverage (without the conflict) for 6 months. This means that your annual HSA contribution limit for 2018 would be 6/12ths of the full annual limit. For example, if you had Single HDHP coverage and are under 55, your full annual HSA contribution limit for 2018 would be $3,450, so your prorated amount for the first six months would be $1,725.
So if you contributed the full $3,450 in February, then by taking the HRA in June, you will have excess HSA contributions of $1,750.
If you stay out of the HRA (you will have to ask the new employer's HR department to see if that is possible), then you continue as before, so long as you keep the HDHP coverage.
How you deal with the excess HSA contributions will depend on whether or not you have already filed for 2018. So I will stop until you can reply as to where you are now.
