Swinton Insurance is halving its Mixenden workforce which will result in the loss of 66 jobs.
Meanwhile, Aldi is opening a new supermarket in Elland next Thursday where 25 jobs have been created.
Swinton confirmed it had begun talks with staff at its outbound call centre where it employs 135.
The company said the changing insurance market had led to the redundancy programme and affected staff are on a 45-day statutory consultation.
The “changing insurance market” refers to more people buying online and the redundancies are part of a programme to cut 120 jobs nationwide from a workforce of 4,500.
A Swinton spokesperson said: “We are pleased, however, that we have managed to safeguard the remaining posts at Mixenden and that it will continue to play a vital role in the company’s planned growth and investment.”
It is the first time the company has reduced numbers through redundancy at the site.
Aldi opens at 8 am on Thursday - and an early morning queue is set to form.
The first 100 customers will be given a golden envelope with each one containing prizes including a 40in HD TV, £50 shopping vouchers and MP3 players.
The store on South Lane, off Huddersfield Road, is one of several Aldi stores opening in West Yorkshire this year, and will carry 1,350 product lines. Aldi won the Which? Award for Best Supermarket 2013.
The latest unemployment figures show falling numbers in Calderdale.
The number of people claiming out-of-work benefits in August has fallen to 5,914.
It’s the sixth month in a row that the figure has fallen.
It is down from 6,067 in July and is made of 3,875 men and 2,039 women.
This is 4.5 per cent of Calderdale’s working population but is above the national average of 3.3 per cent.
The UK rate dropped to 7.7 per cent between May and July from 7.8 per cent in the previous three months.
The Bank of England said interest rates are unlikely to rise before the rate falls to 7 per cent.