On the general side, parliamentary parties (through their whips' offices) play a role in selecting MPs for political offices (such as positions on select committees, as well as more visible roles such as Ministers and Parliamentary Private Secretaries) and physical offices (as in the location in a government building the MP and their staff works from). Depending on the interests of the MP, this might deny them a chance to influence areas on which they feel strongly.If Mr. Ellwood's situation continues past the current Conservative leadership election, it would be unlikely he would be able to stand as a Conservative candidate in a future election.
In this specific case however, the strongest punishment would have been the one mentioned early in the article you cite:
Ellwood will no longer be eligible to vote in the Tory party’s leadership election as he will no longer be regarded as a Conservative MP. He has backed Penny Mordaunt, who came second behind Rishi Sunak, in the latest round of voting on Monday night.
As such, Mr. Ellwood has had his suspension temporarily "un-suspended" to allow him to vote (unsuccessfully) for his preferred candidate.