Only Office 365 Tenant Admins can increase the ‘Rules Quota’ limit for their users, a user himself without the Administrator rights/permissions cannot increase his rules limit. You will need to use Windows PowerShell in Exchange Online to do this. Please see the following article for more help.

Use Windows PowerShell for Exchange Online

For more help and a video walk-thru on how to use Windows PowerShell for Exchange Online, please watch this video.

Office 365 - Troubleshooting PowerShell for Exchange Online 

Below are a couple of commands to use in this scenario.

Current Rules Quota Limit
To determine the current ‘Rules Quota’ limit for a user or mailbox, run the following command in the Windows PowerShell module:

get-mailbox -identity <mailbox> | fl *rulesquota*

where <mailbox> could be the user’s UPN (User Principal Name) or full e-mail address, like john@contoso.onmicrosoft.com as in the example below.

get-mailbox -identity john@contoso.onmicrosoft.com | fl *rulesquota*

The output you can expect to see will be:

RulesQuota : 64 KB (65,536 bytes)

This is the default ‘Rules Quota’ limit for all users in Office 365.

Increase Rules Quota Limit
To increase ‘Rules Quota’ limit for a particular user or mailbox, run the following command in the Windows PowerShell module:

set-mailbox -identity <mailbox> -RulesQuota <xxx>kb

where <mailbox> could be the user’s UPN (User Principal Name) or full e-mail address, like john@contoso.onmicrosoft.com & you can replace <xxx>kb with an appropriate size that you desire for that user, like 150kb, as in the example below.

set-mailbox -identity john@contoso.onmicrosoft.com -RulesQuota 150kb

The maximum ‘Rules Quota’ limit allowed for a user or mailbox is 256KB.

More Information
Tenant Admins can only increase the Inbox Rules Quota limit for their users if their organization’s ‘RBAC Configuration Version’ is higher than 14.16.155. If the above procedure does not work for you, then please use the command below to check your organization’s ‘RBAC Configuration Version’.

Get-organizationconfig | fl *rbacconfigurationversion*

If you see a version lower than 14.16.155, then please contact Office 365 Support to work further on this issue.

We are working to update all related help & knowledge base articles with this information.