The MP has also said it is essential she is kept up to date with any problems that arise during the construction period so they can be dealt with swiftly.
She said: “We now have Royal Assent so we are entering a new phase, but now it is necessary to monitor and scrutinise the construction period on behalf of constituents.
“There is a Code of Construction Practice and we need to ensure that the contractors stick to this code and that any problems which arise are immediately reported and dealt with.
“The next few years will bring a great deal of disruption in the construction areas and as I have obtained an MPs’ Hotline from the Government, I hope people will keep me and the other MPs informed of any problems so that we can deal with them swiftly.
“I am also pleased that I have now got the assurance that our local parish, district and county councils will be reimbursed for the extra costs incurred by them in dealing with HS2 .”
The first phase of the multi-billion pound train project was given the green light on Thursday (Feb 23) following nearly three years of parliamentary scrutiny and debates .
The HS2 Phase 1 Hybrid Bill, the route from London to Birminghan, was granted Royal Assent - the final act before it becomes law.
The House of Lords passed the bill 26-386 during a third debate earlier this month, despite a late bid by peers to derail it.
It was then passed to MPs for a final approval debate on Monday (February 20) where amendments were debated.
The bill received overwhelming support from MPs during its third reading, who passed it 399 to 42 in 2016.
Mrs Gillan has also fought for assurances that parishes and local authorities will be recompensed for the extra spending burdens they are likely to face because of HS2.
She said: “As constituency MP I shall be doing everything within my power to make sure that the funding stream comes through as quickly as possible to our councils who are faced with this disproportionate burden.”