Despite its relatively small size, Qatar is strongly involved in middle eastern politics. The country is ruled by the Al Thani family.
The previous emir, Sheikh Hamad bin Khalifa Al Thani, in power (1995–2013) was a supporter of the Arab Spring in various countries, and was accused by its neighbors of supporting terrorism:
"The news agency released a statement in which it accused Qatar of
“harbouring a multitude of terrorist and sectarian groups that aim to
create instability in the region" . (Al Jazeera)
and
Saudi Arabia, the United Arab Emirates, Bahrain and Egypt severed
diplomatic ties last month with the uber-rich Gulf state of Qatar,
which shares the world’s largest reservoir of gas with Iran, Riyadh’s
hated rival. The bloc accuses Qatar of supporting terrorism, a charge
it denies.
The blockade attempts to cut Qatar off from the rest of the world: the
land border has been sealed, Qatari overflights banned and shipping
lanes closed. The Saudi-led coalition issued 13 demands to lift the
blockade, which included shutting al-Jazeera, the TV voice of the Arab
spring, and dropping support for the Muslim Brotherhood. Despite US
intervention, little has been resolved. (The Guardian)
and
In the wake of the 2011 Arab Spring uprisings, Qatar fell out with
some of its Arab neighbors after it supported the protesters that
sought to overthrow the regimes in several Arab nations. Ties further
deteriorated when Saudi Arabia, Bahrain, the United Arab Emirates and
Egypt severed diplomatic ties with Qatar in mid-2017, accusing the
country of supporting terrorism, which Qatar repeatedly denied. It
took years for the countries to patch up relations. (CNN)
At the same time, Qatar is also maintains an US airbase near Doha.
There were some disagreements within the Al-Thani family itself.
They're trusted by 'revolutionary' organizations like the Hamas, which has had an office in Qatar since 2012 and also receives substantial financial support, and is maintaining public relations with various countries from there, i.e.:
The chairman of the political Ismail Haniyeh burea also holds meeting
with Iranian representatives in Qatar (Iran International)
Despite the support for Hamas, the tone of the articles of the Al-Thani founded Al-Jazeera, indicates that Qatar tries to appear impartial in their support for the Palestinian people:
"Qatar’s foreign minister has said the presence of political leaders
belonging to the Gaza-based Palestinian group Hamas in Doha is
“coordinated with the US” and aimed at facilitating Palestinian unity.
" (AJ)
It appears that the current emir, Sheikh Tamim ibn Hamad Al Thani having access to the Hamas leadership, and currently is pursuing a more subtle policy, which allows him to play a vital role in the current negotiations in which Hamas, Egypt, US and Israel are involved. (CNN) .