Are there specific paremters for the campaign you would like to pause? Perhaps you can create a list of smart list of the leads that you want to pause, and block that smart list from receiving nurture emails for the week.
I have this same question with specific parameters. I want to pause those in the nurture campaign who are assigned to one lead owner, however, I don't want to pause the whole campaign. What is the best way to do this?
Are you using an engagement program? If so you can just create a smart campaign targeting the leads you are interested in (owner =x, member of stream =y, or whatever), and run a flow step to pause them in the stream you are interested in pausing:
In the same smart campaign you can set a wait period and then set their cadence back to normal after whatever time frame you want so they continue to be nurtured.
However if these leads are receiving a series of emails in a regular 'ole smart campaign flow, you can't really pause them. You can just remove them from the flow (using the "remove from flow" flow step) but then they are out completely. You will need to put them back in the beginning or build a separate flow for them to go into later etc.
This is one use case were engagement programs are really great, since they allow so much flexibility.