For using Collector for ArcGIS, is the a licensing cost or agreement needed?
Downloading collector is free.
But I guess you want to sync with ArcGIS Online so you'll need at least an ArcGIS Online account/user
A 'free' ArcGIS Online account comes with each ArcMap license so you might already have some.
Additional arcgis Online licenses can be purchased in bundles of 5. See http://www.esri.com/software/arcgis/arcgisonline/purchase
But, strictly speaking, there are no license costs on Collector as such afaik
You need an organisation AGOL account since the public (free) account does not allow you to create feature services or connect to a FS published on your ArcGIS server.
(Desktop licences come with a nominated AGOL account with 200 credits. Don't confuse them with the public account. Link.)
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