import lxml.etree as ET
content='''\
<div id="contents">
<div id="content_nav">
something goes here
</div>
<p>
some contents
</p>
</div>
'''
tree = ET.fromstring(content, parser=ET.HTMLParser())
contentnav = tree.find(".//div[@id='content_nav']")
contentdiv = contentnav.getparent()
contentdiv.insert(contentdiv.index(contentnav)+1,
ET.XML("<div style='clear: both'></div>"))
print(ET.tostring(tree))
<html><body><div id="contents">
<div id="content_nav">
something goes here
</div>
<div style="clear: both"/><p>
some contents
</p>
</div></body></html>