You can move to a larger package at any time, and there is no penalty for having started smaller.
How to do it
Log in to the client area, go to My Services, choose the service and use the upgrade option. You will be shown the packages available and the cost before confirming anything.
What it costs
You pay only the pro-rata difference between the two packages for the remainder of the period you have already paid for. What you paid for the current package, and how long you have had it, are taken into account and deducted. You are never charged twice for the same period, so there is no financial reason to delay an upgrade you need.
Downtime
None. An upgrade changes the limits on your existing account; nothing is moved and nothing is reinstalled. Your files, databases, email and settings are untouched.
When to upgrade
Before you hit the limits, not after. Exceeding your allowance can lead to the account being suspended automatically, and that is disruptive and entirely avoidable.
Watch Resource Usage in cPanel. If you are regularly close to a limit, that is the moment. See What the resource limits on your account mean.
Check the cause first, though
High usage is often a fixable problem rather than genuine growth – a missing cache, an aggressive bot, or one badly behaved plugin. It is worth ten minutes with Why your site is slow: a general checklist before paying for capacity you may not need. If it turns out you have simply grown, upgrading is the right answer and we will help you pick.
Choosing at the outset
Read the guidance against each package when you first order. Ordering something with too few resources for what you plan to run causes avoidable problems in the first weeks.
Moving to a different type
The same process covers moving from standard hosting to an e-commerce package. If you are unsure which suits you, open a ticket and describe what you are running.