To get Cities: Skylines - Parklife expansion you need to:
- Create a Paradox Account
- Sign up for Paradox newsletter in Settings tab and verify your email
- Sign up for Cities: Skylines newsletter (this option will appear after subscribing to Paradox newsletter)
- Link your Paradox and Steam accounts
- Set your Steam account to "public" and wait up to 36 hours for DLC to appear in your Steam library
You need to own Cities: Skylines game to be able to get Parklife expansion.
Source: Cities: Skylines news on Steam.