While this isn't likely an official part of the position, it's likely a common thing. I believe he's even manned the Conn at least once. To a lesser extent, he's also expected to step into Tactical or Security roles if that position is unexpectedly vacated. He has access and knowledge of ship protocols almost identical to Picard's, so he has to keep on top of that. Riker also has to be ready to step up into Picard's role at the drop of a hat. The two of them work as checks against each-other, with the department heads/senior staff adding another layer.
If someone doesn't jive between the two, it could point to a coverup. Riker's logs and reports provide an important second POV to Picard's. Picard gets final say, but I'd assume he trusts Riker's judgment in most cases. Riker approves/denies transfers (inter and intra ship), at least on a preliminary basis. If someone steps out of line and the department head can't resolve it themselves, it falls to Riker. Riker also deals with ship discipline, like an HR department.
Department heads work with him to draw up duty rosters and allocate resources.
Riker is in charge of day-to-day operations and coordination across the ship. If anything, Riker's existence makes Picard's role somewhat redundant. PO Box, APO/FPO, Afghanistan, Alaska/Hawaii, Albania, Algeria, American Samoa, Andorra, Angola, Anguilla, Antigua and Barbuda, Argentina, Armenia, Aruba, Australia, Austria, Azerbaijan Republic, Bahamas, Bahrain, Bangladesh, Barbados, Belarus, Belgium, Belize, Benin, Bermuda, Bhutan, Bolivia, Bosnia and Herzegovina, Botswana, Brazil, British Virgin Islands, Brunei Darussalam, Bulgaria, Burkina Faso, Burundi, Cambodia, Cameroon, Canada, Cape Verde Islands, Cayman Islands, Central African Republic, Chad, Chile, China, Colombia, Comoros, Congo, Democratic Republic of the, Congo, Republic of the, Cook Islands, Costa Rica, Croatia, Republic of, Cyprus, Czech Republic, Côte d'Ivoire (Ivory Coast), Denmark, Djibouti, Dominica, Dominican Republic, Ecuador, Egypt, El Salvador, Equatorial Guinea, Eritrea, Estonia, Ethiopia, Falkland Islands (Islas Malvinas), Fiji, Finland, France, French Guiana, French Polynesia, Gabon Republic, Gambia, Georgia, Germany, Ghana, Gibraltar, Greece, Greenland, Grenada, Guadeloupe, Guam, Guatemala, Guernsey, Guinea, Guinea-Bissau, Guyana, Haiti, Honduras, Hong Kong, Hungary, Iceland, India, Indonesia, Iraq, Ireland, Israel, Italy, Jamaica, Japan, Jersey, Jordan, Kazakhstan, Kenya, Kiribati, Korea, South, Kuwait, Kyrgyzstan, Laos, Latvia, Lebanon, Lesotho, Liberia, Libya, Liechtenstein, Lithuania, Luxembourg, Macau, Macedonia, Madagascar, Malawi, Malaysia, Maldives, Mali, Malta, Marshall Islands, Martinique, Mauritania, Mauritius, Mayotte, Mexico, Micronesia, Moldova, Monaco, Mongolia, Montenegro, Montserrat, Morocco, Mozambique, Namibia, Nauru, Nepal, Netherlands, Netherlands Antilles, New Caledonia, New Zealand, Nicaragua, Niger, Nigeria, Niue, Norway, Oman, Pakistan, Palau, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Poland, Portugal, Puerto Rico, Qatar, Reunion, Romania, Russian Federation, Rwanda, Saint Helena, Saint Kitts-Nevis, Saint Lucia, Saint Pierre and Miquelon, Saint Vincent and the Grenadines, San Marino, Saudi Arabia, Senegal, Serbia, Seychelles, Sierra Leone, Singapore, Slovakia, Slovenia, Solomon Islands, Somalia, South Africa, Spain, Sri Lanka, Suriname, Svalbard and Jan Mayen, Swaziland, Sweden, Switzerland, Taiwan, Tajikistan, Tanzania, Thailand, Togo, Tonga, Trinidad and Tobago, Tunisia, Turkey, Turkmenistan, Turks and Caicos Islands, Tuvalu, US Protectorates, Uganda, Ukraine, United Arab Emirates, United Kingdom, Uruguay, Uzbekistan, Vanuatu, Vatican City State, Venezuela, Vietnam, Virgin Islands (U.S.What? No.