From what I read from https://support.upwork.com/hc/en-us/articles/211062898-Use-Connects, it seems that the following are your options:
1. Wait for a client to invite you - and this means tinkering with your availability settings.
2. Wait for a project to be cancelled. Two connects will be returned to your account for each project that is cancelled (either by Upwork or by the client).
3. Upgrade to a Plus Membership Plan. This option will make your monthly excess connects be rolled over for future use.
4. Wait for an "old" client to come back and assign an new task to you.
5. Wait for the system to reset your connects.
Am I making sense?
Have you used connects before? Have you applied to jobs already? Did you have connects in April? I don't know how recent your profile is, but it may not have been approved yet, which is why you still don't have connects. That's why I'm asking these questions.
I had connects before in the month of April. I have applied to many jobs before and now they are finished. One of the applied job is active too. I don't think my profile is still under review. Thank you for your support.
It renews monthly from the day you started your membership.