Unfortunately, whilst a season ticket from Chelmsford to London Terminals
should logically be valid into St Pancras, there is a negative easement which prevents this from being the case on Any Permitted tickets.
When HS1 opened, Southeastern quickly had this easement added, as they feel that HS1 justifies a huge premium and aren't happy with "normal" ticket holders using it!
Fortunately, there is at least the option of buying a season ticket specifically issued to St Pancras, routed +Plus High Speed, which would be valid on HS1 into St Pancras.
It's priced at rather a premium compared to the Any Permitted (£142.60 a week vs £112) - whether this (or indeed any season ticket at all) is worthwhile will depend on the travel facilities available to you, how often you'll be travelling to work and whether you'll often be travelling in/out at times when an Off-Peak ticket would be valid.
Good luck in the new job!
The validity is only to Liverpool Street
It's also valid to Fenchurch Street, though only via the rarely-served Stratford-Limehouse link (Gas Factory Jn might ring a bell
@martin2345uk )