It's not an app only, it's an online service that offers apps for different platforms: Have a look at Freshbooks.
It will let you add clients and as many projects as you want for each clients. You can choose different currency for each client and also have many logins for one single client (eg. for members of their own team).
Clients and collaborators can get access to your online time sheets and other reports. Member areas are private. You can also see who logged in and a feed of activity.
For you own team, it's possible to download apps with timers that are linked to each clients and projects; you can use the apps with specific tasks and the online time sheet will get updated automatically. You can also add a note within the timer app about what you're working on and the note will be added to the time sheet as well.
There's some free versions for the time tracking app but you can also purchase other apps at low cost. Or build your own. The default one works perfectly fine.
It's also possible to have different price for each task or project. Prices can be flat per/project or per/hour or per/task.
You can also add/upload expenses related to a project. Clients will be able to see these expenses.
There's a simple "ticket/dispute" system as well.
Finally, when a project is completed, you can use Freshbooks to invoice your client; it will let you calculate and prepare automatically a detailed invoice with all the time and task entries, and calculate the total for you. Clients will be able to pay online and you can use different payment gateway (WePay, Paypal, Stripe, etc.) It creates an invoice in PDF file and clients can see all their previous invoices online in their member areas. You can send the invoice by email or snail mail; Freshbooks will mail for you.
Their customer support is also amazing.
Time Tracking details:
PS: I use it for many years, it's certainly one of the biggest time saver to manage projects. I've tried a few timers and this one has always been the easiest to use for both clients and my team, and the timer app is great.