Nixie cryptic clues to solve, Set 1

I have decided to close my 'Twitface' accounts (Twitter and author's page on Facebook) in the interests of less stress, and more simplicity in my life. I will still be posting cryptic clues that you can solve here, and will be updating this blog more frequently too. I look forward to continuing conversations with my friends from those other social networks – welcome!

Here's the first batch. Let me know how you get on in the Comments, and I'm happy to provide hints if anyone needs them.

I will post answers in a few days  :)
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1) Gulps down birds (8)

2) Worker has loud grievance (4)

3) Endless blaze leaves a tree (3)

4) Relation at the ABC? (6)

5) Mourn appropriately if making livery (7)

6) Cable tram stuffed with unrestrained glee (8)

7) Émigré Patrick went after former wife (5)


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